Persistent order due to transiently enhanced nesting in an electronically excited charge density wave

Structural dynamics at surfaces by ultrafast reflection high-energy electron diffraction

Many fundamental processes of structural changes at surfaces occur on a pico- or femtosecond timescale. In order to study such ultrafast processes, we have combined modern surface science techniques with fs-laser pulses in a pump-probe scheme. Grazing incidence of the electrons ensures surface sensitivity in ultrafast reflection high-energy electron diffraction (URHEED). Utilizing the Debye-Waller effect, we studied the nanoscale heat transport from an ultrathin film through a hetero-interface or the damping of vibrational excitations in monolayer adsorbate systems on the lower ps-timescale. By means of spot profile analysis, the different cooling rates of epitaxial Ge nanostructures of different size and strain state were determined. The excitation and relaxation dynamics of a driven phase transition far away from thermal equilibrium is demonstrated using the In-induced (8 × 2) reconstruction on Si(111). This Peierls-distorted surface charge density wave system exhibits a discontinuous phase transition of first order at 130 K from a (8 × 2) insulating ground state to (4 × 1) metallic excited state. Upon excitation by a fs-laser pulse, this structural phase transition is non-thermally driven in only 700 fs into the excited state. A small barrier of 40 meV hinders the immediate recovery of the ground state, and the system is found in a metastable supercooled state for up to few nanoseconds.

Charge density wave induced nodal lines in LaTe3

LaTe₃ is a non-centrosymmetric material with time reversal symmetry, where the charge density wave is hosted by the Te bilayers. Here, we show that LaTe₃ hosts a Kramers nodal line-a twofold degenerate nodal line connecting time reversal-invariant momenta. We use angle-resolved photoemission spectroscopy, density functional theory with an experimentally reported modulated structure, effective band structures calculated by band unfolding, and symmetry arguments to reveal the Kramers nodal line. Furthermore, calculations confirm that the nodal line imposes gapless crossings between the bilayer-split charge density wave-induced shadow bands and the main bands. In excellent agreement with the calculations, spectroscopic data confirm the presence of the Kramers nodal line and show that the crossings traverse the Fermi level. Furthermore, spinless nodal lines-completely gapped out by spin-orbit coupling-are formed by the linear crossings of the shadow and main bands with a high Fermi velocity.

Exploring the Charge Density Wave Phase of 1T-TaSe_{2}: Mott or Charge-Transfer Gap?

1T-TaSe_{2} is widely believed to host a Mott metal-insulator transition in the charge density wave (CDW) phase according to the spectroscopic observation of a band gap that extends across all momentum space. Previous investigations inferred that the occurrence of the Mott phase is limited to the surface only of bulk specimens, but recent analysis on thin samples revealed that the Mott-like behavior, observed in the monolayer, is rapidly suppressed with increasing thickness. Here, we report combined time- and angle-resolved photoemission spectroscopy and theoretical investigations of the electronic structure of 1T-TaSe_{2}. Our experimental results confirm the existence of a state above E_{F}, previously ascribed to the upper Hubbard band, and an overall band gap of ∼0.7  eV at Γ[over ¯]. However, supported by density functional theory calculations, we demonstrate that the origin of this state and the gap rests on band structure modifications induced by the CDW phase alone, without the need for Mott correlation effects.

Origin of Immediate Damping of Coherent Oscillations in Photoinduced Charge-Density-Wave Transition

In stark contrast to the conventional charge density wave (CDW) materials, the one-dimensional CDW on the In/Si(111) surface exhibits immediate damping of the CDW oscillation during the photoinduced phase transition. Here, we successfully reproduce the experimental observation of the photoinduced CDW transition on the In/Si(111) surface by performing real-time time-dependent density functional theory (rt-TDDFT) simulations. We show that photoexcitation promotes valence electrons from the Si substrate to the empty surface bands composed primarily of the covalent p-p bonding states of the long In-In bonds. Such photoexcitation generates interatomic forces to shorten the long In-In bonds and thus drives the structural transition. After the structural transition, these surface bands undergo a switch among different In-In bonds, causing a rotation of the interatomic forces by about π/6 and thus quickly damping the oscillations in feature CDW modes. These findings provide a deeper understanding of photoinduced phase transitions.

Square-Net Topological Semimetals: How Spectroscopy Furthers Understanding and Control

Square-net materials are well positioned to lead optical spectroscopic explorations into the electronic structure, photoinduced dynamics, and phase transitions in topological semimetals. Hundreds of square-net topological semimetals can be prepared that have remarkably different electronic and optical properties despite having similar structures. Here we present what has been gleaned recently from these materials with the whole gamut of optical spectroscopies, ranging from steady-state reflectance and Raman investigations into topological band structures, electronic correlations, and equilibrium phase transitions to time-resolved techniques used to decipher ultrafast relaxation dynamics and nonequilibrium photoinduced phase transitions. We end with a discussion of some major remaining questions and possible future research directions.

Coherent Modulation of Quasiparticle Scattering Rates in a Photoexcited Charge-Density-Wave System

We present a complementary experimental and theoretical investigation of relaxation dynamics in the charge-density-wave (CDW) system TbTe_{3} after ultrafast optical excitation. Using time- and angle-resolved photoemission spectroscopy, we observe an unusual transient modulation of the relaxation rates of excited photocarriers. A detailed analysis of the electron self-energy based on a nonequilibrium Green's function formalism reveals that the phase space of electron-electron scattering is critically modulated by the photoinduced collective CDW excitation, providing an intuitive microscopic understanding of the observed dynamics and revealing the impact of the electronic band structure on the self-energy.

Time-resolved structural dynamics of the out-of-equilibrium charge density wave phase transition in GdTe3

We use ultrafast electron diffraction to study the out-of-equilibrium dynamics of the charge density wave (CDW) phase transition in GdTe3, a quasi-two-dimensional compound displaying a unidirectional CDW state. Experiments were conducted at different incident fluences and different initial sample temperatures below Tc. We find that following photo-excitation, the system undergoes a non-thermal ultrafast phase transition that occurs in out-of-equilibrium conditions. The intrinsic crystal temperature was estimated at each time delay from the atomic thermal motion, which affects each Bragg peak intensity via the Debye Waller factor. We find that the crystal temperature stabilizes with a 6 ps timescale in a quasi-equilibrium state at temperature T q . e . . We then relate the recovery time of the CDW and its correlation lengths as a function of T q . e . . The charge density wave is suppressed in less than a picosecond while its recovery time increases linearly with incident fluence and initial temperature. Our results highlight that the dynamics is strongly determined by the initial sample temperature. In addition, the transient CDW phase recently observed along the transverse direction in LaTe3 and CeTe3 is not observed in GdTe3.

Role of Equilibrium Fluctuations in Light-Induced Order

Engineering novel states of matter with light is at the forefront of materials research. An intensely studied direction is to realize broken-symmetry phases that are "hidden" under equilibrium conditions but can be unleashed by an ultrashort laser pulse. Despite a plethora of experimental discoveries, the nature of these orders and how they transiently appear remain unclear. To this end, we investigate a nonequilibrium charge density wave (CDW) in rare-earth tritellurides, which is suppressed in equilibrium but emerges after photoexcitation. Using a pump-pump-probe protocol implemented in ultrafast electron diffraction, we demonstrate that the light-induced CDW consists solely of order parameter fluctuations, which bear striking similarities to critical fluctuations in equilibrium despite differences in the length scale. By calculating the dynamics of CDW fluctuations in a nonperturbative model, we further show that the strength of the light-induced order is governed by the amplitude of equilibrium fluctuations. These findings highlight photoinduced fluctuations as an important ingredient for the emergence of transient orders out of equilibrium. Our results further suggest that materials with strong fluctuations in equilibrium are promising platforms to host hidden orders after laser excitation.

Nonequilibrium charge-density-wave order beyond the thermal limit

The interaction of many-body systems with intense light pulses may lead to novel emergent phenomena far from equilibrium. Recent discoveries, such as the optical enhancement of the critical temperature in certain superconductors and the photo-stabilization of hidden phases, have turned this field into an important research frontier. Here, we demonstrate nonthermal charge-density-wave (CDW) order at electronic temperatures far greater than the thermodynamic transition temperature. Using time- and angle-resolved photoemission spectroscopy and time-resolved X-ray diffraction, we investigate the electronic and structural order parameters of an ultrafast photoinduced CDW-to-metal transition. Tracking the dynamical CDW recovery as a function of electronic temperature reveals a behaviour markedly different from equilibrium, which we attribute to the suppression of lattice fluctuations in the transient nonthermal phonon distribution. A complete description of the system's coherent and incoherent order-parameter dynamics is given by a time-dependent Ginzburg-Landau framework, providing access to the transient potential energy surfaces.

Nonequilibrium dynamics of spontaneous symmetry breaking into a hidden state of charge-density wave

Nonequilibrium phase transitions play a pivotal role in broad physical contexts, from condensed matter to cosmology. Tracking the formation of nonequilibrium phases in condensed matter requires a resolution of the long-range cooperativity on ultra-short timescales. Here, we study the spontaneous transformation of a charge-density wave in CeTe₃ from a stripe order into a bi-directional state inaccessible thermodynamically but is induced by intense laser pulses. With ≈100 fs resolution coherent electron diffraction, we capture the entire course of this transformation and show self-organization that defines a nonthermal critical point, unveiling the nonequilibrium energy landscape. We discuss the generation of instabilities by a swift interaction quench that changes the system symmetry preference, and the phase ordering dynamics orchestrated over a nonadiabatic timescale to allow new order parameter fluctuations to gain long-range correlations. Remarkably, the subsequent thermalization locks the remnants of the transient order into longer-lived topological defects for more than 2 ns.

A quantitative comparison of time-of-flight momentum microscopes and hemispherical analyzers for time- and angle-resolved photoemission spectroscopy experiments

Time-of-flight-based momentum microscopy has a growing presence in photoemission studies, as it enables parallel energy- and momentum-resolved acquisition of the full photoelectron distribution. Here, we report table-top extreme ultraviolet time- and angle-resolved photoemission spectroscopy (trARPES) featuring both a hemispherical analyzer and a momentum microscope within the same setup. We present a systematic comparison of the two detection schemes and quantify experimentally relevant parameters, including pump- and probe-induced space-charge effects, detection efficiency, photoelectron count rates, and depth of focus. We highlight the advantages and limitations of both instruments based on exemplary trARPES measurements of bulk WSe₂. Our analysis demonstrates the complementary nature of the two spectrometers for time-resolved ARPES experiments. Their combination in a single experimental apparatus allows us to address a broad range of scientific questions with trARPES.

High resolution time- and angle-resolved photoemission spectroscopy with 11 eV laser pulses

Performing time- and angle-resolved photoemission (tr-ARPES) spectroscopy at high momenta necessitates extreme ultraviolet laser pulses, which are typically produced via high harmonic generation (HHG). Despite recent advances, HHG-based setups still require large pulse energies (from hundreds of μJ to mJ) and their energy resolution is limited to tens of meV. Here, we present a novel 11 eV tr-ARPES setup that generates a flux of 5 × 10¹⁰ photons/s and achieves an unprecedented energy resolution of 16 meV. It can be operated at high repetition rates (up to 250 kHz) while using input pulse energies down to 3 µJ. We demonstrate these unique capabilities by simultaneously capturing the energy and momentum resolved dynamics in two well-separated momentum space regions of a charge density wave material ErTe₃. This novel setup offers the opportunity to study the non-equilibrium band structure of solids with exceptional energy and time resolutions at high repetition rates.

Charge Density Wave Melting in One-Dimensional Wires with Femtosecond Subgap Excitation

Charge density waves (CDWs) are symmetry-broken ground states that commonly occur in low-dimensional metals due to strong electron-electron and/or electron-phonon coupling. The nonequilibrium carrier distribution established via photodoping with femtosecond laser pulses readily quenches these ground states and induces an ultrafast insulator-to-metal phase transition. To date, CDW melting has been mainly investigated in the single-photon regime with pump photon energies bigger than the gap size. The recent development of strong-field midinfrared sources now enables the investigation of CDW dynamics following subgap excitation. Here we excite prototypical one-dimensional indium wires with a CDW gap of ∼300  meV with midinfrared pulses at ℏω=190  meV with MV/cm field strength and probe the transient electronic structure with time- and angle-resolved photoemission spectroscopy. We find that the CDW gap is filled on a timescale short compared to our temporal resolution of 300 fs and that the band structure changes are completed within ∼1  ps. Supported by a minimal theoretical model we attribute our findings to multiphoton absorption across the CDW gap.

Combining time-resolved optical (TOS), electronic (trARPES) and structural (UED) probes on the class of rare earth tritellurides RTe3

The combination of EUV based time-resolved Angle-Resolved-Photo-Electron-Spectroscopy (trARPES), Ultrafast-Electron-Diffraction (UED) and Transient-Optical-Spectroscopy (TOS) facilitates a comprehensive study and all-embracing analysis of correlated dynamics, exemplified on the system of Charge-Density-Waves (CDW’s) in rare earth tritellurides (RTe3).

High repetition pump-and-probe photoemission spectroscopy based on a compact fiber laser system

The paper describes a time-resolved photoemission (TRPES) apparatus equipped with a Yb-doped fiber laser system delivering 1.2-eV pump and 5.9-eV probe pulses at the repetition rate of 95 MHz. Time and energy resolutions are 11.3 meV and ∼310 fs, respectively, the latter is estimated by performing TRPES on a highly oriented pyrolytic graphite (HOPG). The high repetition rate is suited for achieving high signal-to-noise ratio in TRPES spectra, thereby facilitating investigations of ultrafast electronic dynamics in the low pump fluence (p) region. TRPES of polycrystalline bismuth (Bi) at p as low as 30 nJ/mm² is demonstrated. The laser source is compact and is docked to an existing TRPES apparatus based on a 250-kHz Ti:sapphire laser system. The 95-MHz system is less prone to space-charge broadening effects compared to the 250-kHz system, which we explicitly show in a systematic probe-power dependency of the Fermi cutoff of polycrystalline gold. We also describe that the TRPES response of an oriented Bi(111)/HOPG sample is useful for fine-tuning the spatial overlap of the pump and probe beams even when p is as low as 30 nJ/mm².

Ultrafast Spin Density Wave Transition in Chromium Governed by Thermalized Electron Gas

The energy and momentum selectivity of time- and angle-resolved photoemission spectroscopy is exploited to address the ultrafast dynamics of the antiferromagnetic spin density wave (SDW) transition photoexcited in epitaxial thin films of chromium. We are able to quantitatively extract the evolution of the SDW order parameter Δ through the ultrafast phase transition and show that Δ is governed by the transient temperature of the thermalized electron gas, in a mean field description. The complete destruction of SDW order on a sub-100 fs time scale is observed, much faster than for conventional charge density wave materials. Our results reveal that equilibrium concepts for phase transitions such as the order parameter may be utilized even in the strongly nonadiabatic regime of ultrafast photoexcitation.